High information content imaging using Mie photo sensors

ABSTRACT

A Mie photo sensor is described. A Mie photo sensor is configured to leverage Mie scattering to implement a photo sensor having a resonance. The resonance is based on various physical and material properties of the Mie photo sensor. In an example, a Mie photo sensor includes a layer of semiconductor material with one or more mesas. Each mesa of semiconductor material may include a scattering center. The scattering center is formed by the semiconductor material of the mesa being at least partially surround by a material with a different refractive index than the semiconductor material. The abutting refractive index materials create an interface that forms a scattering center and localizes the generation of free carriers during Mie resonance. One or more electrical contacts may be made to the mesa to measure the electrical properties of the mesa.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional application No.62/720,002 filed on Aug. 20, 2018, which is incorporated in its entiretyby this reference.

GOVERNMENT RIGHTS LEGEND

This invention was made with government support under Federal AwardIdentification Number 1660145 awarded by the National ScienceFoundation. The government has certain rights in the invention.

BACKGROUND 1. Technical Field

This disclosure relates generally to a photo-sensitive device, and moreparticularly, to an array of photo-sensitive devices for generatingimages.

2. Description of the Related Art

Conventional photo sensors operate at size scales where sensor elementsthat interact with incident light are much larger than the light'swavelength. For example, conventional photo sensors are on the order ofa micron in size to sense light at visible wavelengths. At these sizes,Snell's law of refraction holds, and the absorption of incident light ona photo sensor follows the Beer-Lambert law. Many attempts at designingphoto sensor to minimize their physical size, but the resulting sensorsoften have many drawbacks. For example, the signal-to-noise ratio,dynamic range, depth of field, and depth of focus, all deteriorate whengenerating images with photo sensors of decreased size. Accordingly, aphoto sensor with decreased size that is able generate high qualityimages would be beneficial.

SUMMARY

A Mie photo sensor is described. A Mie photo sensor leverages Miescattering to generate improved photo currents relative to conventionalphoto sensor technologies as described herein. A Mie photo sensorcomprises a substrate of a material (i.e., a material layer) such as asemiconductor or an insulator. The material layer has a first index ofrefraction and comprises a mesa of semiconducting material. The mesa isconfigured to generate free carriers within the semiconducting materialin response to an electromagnetic perturbation (e.g., incident light,x-rays, etc.).

The Mie photo sensor also comprise a refractive medium surrounding thematerial layer. The refractive medium may have a complex index ofrefraction. The refractive medium abuts the mesa and forms an interfacewith an index of refraction across the interface that is discontinuous.Additionally, the refractive medium defines an electromagneticscattering center (e.g., the mesa, or some portion of the mesa)configured for generating free carriers via optical absorption and Mieresonance of the electromagnetic perturbation at the scattering center.

In an example embodiment, the refractive profiles of the Mie photosensors are described as follows: the material layer has a first indexof refraction, the mesa of semiconducting material has a second index ofrefraction, and the refractive medium has a third index of refraction.The index of refraction for the refractive medium is generally complexand may be discontinuous across the boundary between the mesa and therefractive material. In an example, the third index of refraction isless than the first index of refraction and the second index ofrefraction. In another example, the first index of refraction is thesame as the second index of refraction.

In an example embodiment, the mesa of semiconductor layer forms ageometric shape (e.g., a rectangular prism, a cube, etc.) having a setof boundaries which abut the refractive medium. As such, theelectromagnetic scattering center is formed either at the boundaries ofthe shape, or within the boundaries of the shape, such that theelectromagnetic scattering center comprises some portion (or all) ofsemiconducting material of the mesa.

In an example embodiment, the material layer comprises silicon and themesa comprises doped silicon. In another example embodiment, thematerial layer comprises silicon dioxide and the mesa comprises silicon.Other example embodiments are also possible.

Various physical characteristics of the scattering center influencewhich electromagnetic perturbations are absorbed by the material of thescattering center and, thereby, generate free carriers. For example, thedimensions of the mesa may affect the wavelength and polarization ofelectromagnetic perturbations that may be absorbed by the scatteringcenter.

The Mie photo sensor also comprises one or more electrical contactscoupled to the mesa and configured to sense free carriers generatedwithin the scattering center in response to the electromagneticperturbation. There are several example configurations of contactspossible. In a first example, a first contact of the electrical contactsforms an Ohmic contact with the mesa and a second contact forms aSchottky barrier with the mesa. In a second example, a first contactforms an Ohmic contact with the mesa and a second contact forms a p-njunction with the mesa. In a third example, a first contact and a secondcontact form an Ohmic contact with the mesa of semiconductor material.In this case, the Mie photo sensor includes a p-n junction at a boundarybetween the refractive material and the mesa of semiconducting material.

The Mie photo sensor operates in a resonance fashion, where theresonance is based on any of the factors described herein. For example,the electromagnetic scattering center absorbs a particular wavelength ofelectromagnetic perturbation at a resonance level and generates a firstamount of free carriers corresponding the resonance level. Additionally,the electromagnetic scattering center absorbs a different wavelength ofelectromagnetic perturbation at a non-resonance level and generates asecond amount of free carriers corresponding to the non-resonance level.In this situation, the first amount of free electrons is greater thanthe second amount of free electrons.

Further, a Mie photo sensor is configured to localize carrier generationin a scattering center as described herein. That is, the absorption ofthe electromagnetic perturbation in the electromagnetic scatteringcenter is higher than the absorption of the electromagnetic perturbationin both the semiconductor layer and the refractive medium. For example,

a first amount of free carriers generated by the absorption of theelectromagnetic perturbation in the electromagnetic scattering center isgreater than a second amount of carriers are generated by theelectromagnetic perturbation in the semiconductor layers.

Additionally, the Mie photo sensors can be connected to various controlelectronics to create a pixel. Multiple pixels may be connected to oneanother to form an image sensor. For various reasons described herein,an image sensor including pixels created with Mie photo sensors operatesbetter than their conventional counterparts.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure have other advantages and features whichwill be more readily apparent from the following detailed descriptionand the appended claims, when taken in conjunction with the accompanyingdrawings, in which:

FIGS. 1A-1H illustrate a series of resonance plots, according to severalexample embodiments.

FIG. 2 illustrates an absorbed power plot for a rectilinear Mie photosensor, according to one example embodiment.

FIG. 3A illustrates top down view of a Mie photo sensor, according toone example embodiment.

FIG. 3B illustrates a side view of a Mie photo sensor, according to oneexample embodiment.

FIG. 4 illustrates a voltage response plot for a Mie photo sensor,according to one example embodiment.

FIG. 5 is a voltage multi-response plot, according to one exampleembodiment, according to one example embodiment.

FIG. 6 illustrates a cross-sectional field plot 600 of a Mie photosensor, according to one example embodiment, according to one exampleembodiment.

FIG. 7 illustrates a Mie photo sensor, according to one exampleembodiment, according to one example embodiment.

FIG. 8 is a cross-sectional field plot of a Mie photo sensor, accordingto one example embodiment, according to one example embodiment.

FIG. 9 illustrates a voltage multi-response plot, according to oneexample embodiment, according to one example embodiment.

FIGS. 10A-10C illustrate various configurations of a Mie photo sensor,according to some example embodiments.

FIGS. 11A-11E illustrate several different configurations for a pixel inan image sensor including one or more Mie photo sensors, according tovarious example embodiments.

The figures depict various embodiments for purposes of illustrationonly. One skilled in the art will readily recognize from the followingdiscussion that alternative embodiments of the structures and methodsillustrated herein may be employed without departing from the principlesdescribed herein.

DETAILED DESCRIPTION

I. Introduction

Photo sensor arrays are composed of a surface including a number ofpixels where each pixel may comprise a photo sensor and signalcollection electronics that are, generally, approximately co-locatedwith each photo sensor. Each pixel operates by detecting photons atparticular wavelengths and then generating an electrical charge,voltage, or resistance that is related to the number of photons detectedat each pixel. This charge, voltage, or resistance is then measured,digitized, and used to construct an image of the object, scene, orphenomenon that emitted or reflected the photons. Photo sensors can alsobe deployed for imaging as single detector or as an array of detectors.

Future photo sensor technology adoption may be fueled by, for example,three primary ideas: i) image quality (e.g., resolution, low lightperformance, multispectral imaging, etc.), ii) pixel size inthree-dimensions, and, 3) device functionality (e.g., high-speed video,image analysis, motion control, cost, Size, Weight, and Power (SWaP),etc.). Innovation in each of these areas includes design decisions atevery level. Example design decisions may include, for example, thestructure and device physics of the photo sensing element (i.e., photondetection), the basic operation of the pixel (i.e., signal capture,storage, and transfer) and the design and operation of the imaging array(i.e., image readout and signal processing).

At each of these levels, significant challenges remain for improvingperformance. For example, the challenges may include improvingperformance tradeoffs between a set of devices, device processes, and acircuit (or circuits) made of those devices. Furthermore, the challengesare becoming more apparent as image processing moves into a new erawhere design emphasis goes beyond image data to information-centricimage sensors (e.g., computational image sensors, silicon retinasembedded in smart vision systems, etc.). Market drivers for imagesensors are pushing for embedded computer vision pre-processingfunctions, improved response times and minimized SWaP for a large set ofvision systems that include wireless sensor networks, unattendedsurveillance networks, automotive, internet-of-things and other portablevision applications.

II. Current Photo Sensor Technologies, Optimizations and Tradeoffs

II.A the Structure and Device Physics of Photo Sensors

For imaging visible light, the underlying photo-sensing process beginswith light absorption in a semiconductor. The process is, generally,similar for imaging in the x-ray, ultraviolet, and infrared portions ofthe spectrum. The absorbed light generates an electron-hole pair and theconstituent electron and hole are separated in space by an electricfield in a depletion region in the semiconductor. Depletion regions canbe formed by varying properties in a semiconductor system (e.g., asemiconductor junction) or using a semiconductor-metal junction (e.g., aSchottky junction).

Conventional photo sensors operate in the realm of physical optics whereindividual sensor elements that interact with incident light are muchlarger than the light's wavelength. In this regime, Snell's law ofrefraction holds, the absorption of radiation follows the Beer-Lambertlaw, and scattering is proportional to the projected physical area ofthe scattering element. For photo detectors in this regime to act as aneffective light absorber, the semiconductor that comprises the photosensor must be optically thick. That is, the probability that a photonis absorbed in a layer of semiconductor is1−e ^(−αd)  (1)where α is an absorption coefficient that depends on both the incidentlight's wavelength and the absorbing material's composition, and d isthe layer thickness along the direction of incident light. A usefulestimate for a minimum layer thickness is α⁻¹, at which around 60% ofthe incident light is absorbed in the photo sensor.

Silicon is a versatile and economically viable semiconductor materialfor visible light photo sensors. Across the visible spectrum theabsorption coefficient of silicon varies from about 10⁵ cm⁻¹ at 390 nmto about 10³ cm⁻¹ at 700 nm. For silicon, the absorption coefficientsindicate that a semiconductor thickness should be about 1 μm to absorbaround 60% of the incident light.

A semiconductor thickness of around 1 μm introduces several problems forimproving image sensors (e.g., size, response, etc.). One problem stemsfrom commercially feasible semiconductor fabrication processes rely onphotolithography. Photolithography is best for planer or pseudo-planerstructures. For example, approximately planer structures (e.g., photosensors) with planer features on the order of, or larger than, verticalfeatures (i.e., out of the plane). As a result, because the verticaldimension for good absorption for a silicon is approximately 1 μm,planer photo sensor dimensions are also, generally, on the order of 1μm. Therefore, while the dimension in the plane can be reduced somewhat,photo sensor sizes are difficult to substantially reduce below 1 μm.Another problem stemming from thick sensors is that thick sensors limitthe possibility of using vertical layers of stacked arrays. For example,having a stack of three sensor arrays, each with a thickness of 1 μmyields a stack height of 3 μm. In this case, absorption of light in oneor more of the layers may be reduced because of the thickness of thestack. However, if stacked arrays substantially thinner than 1 μm couldbe implemented, various benefits could be seen. For example, a stack ofthink layers would allow the layers to deconvolve chromic aberrations inassociated imaging optics.

Photo sensors may also use other materials with higher absorptioncoefficients. As an example, in the visible spectrum, gallium arsenide'sabsorption coefficient ranges from about 10⁵ to 10⁶ cm⁻¹. This suggeststhat a 0.1 μm thick semiconductor will deliver a 1/e absorptionprobability. However, there are still several drawbacks to galliumarsenide. For example, gallium arsenide is the second most commonsemiconductor utilized by the semiconductor industry and is, generally,much more expensive than silicon. In addition, fabrication of galliumarsenide features at length scales significantly less than 1 μm is verychallenging and commercial implementation is uncommon. Finally, creatingohmic contacts to gallium arsenide (for electrical connections) withdimensions significantly smaller than 1 μm is difficult and hasexhibited unacceptably low yields.

One way to improve the imaging performance of photo-sensitive arrays isto make large pixels while, at the same time, keeping the overall pixelcount constant. Cameras used in some scientific applications have pixelswith linear dimensions of 15 μm or more. These large pixel sizes enablean improvement in dynamic range and noise. However, larger pixel sizesare counter to current market drivers and come at the cost of bothcamera size and expense. To maintain similar imaging properties for acamera using a sensor array comprised of 1 μm pixels, a detector with 15μm pixels has an area approximately 200 times larger, and the imagingoptics volume is approximately 3000 times larger. Both of theseimplications (e.g., size and volume) severely limit the extent to whichsuch a solution for improving photo sensors can be utilized. Forexample, in practice, implementing significantly larger pixels is oftenaccompanied by a decrease in pixel count, a decrease in maximumfield-of-view, or both.

Another method to improve photo sensor performance is to increase photosensor light sensitivity (e.g., low light intensity measurements) byutilizing avalanche effects in the photo sensor. That is, appliedvoltages are used to generate high electric fields in the semiconductorand increased light sensitivities occur in response. The high fieldsaccelerate photo-generated carriers to significantly higher velocitiesthan would be attained otherwise. Subsequent collisions createadditional free carriers which are accelerated in turn. As a result,single incident photons can generate a substantial output signal. Whilesuch photo sensors can achieve very high sensitivity, they are oftenoperated in Geiger mode which yields a dynamic range of 0 dB. Otherwise,such devices are operated in proportional mode which can deliver adynamic range of up to 60 dB, but only for an incident intensity rangeof about 1 to 1000 photons/measurement interval.

Plasmonic materials have also been explored as a method for amplifyingthe light incident on the photo sensor. In this case the photo sensorproduces surface excitations of electrons enabling conductors tostrongly absorb, and subsequently re-radiate, the incident light.Plasmonics utilizes strong resonances that can be tailored topreferentially interact with specific combinations of incidentwavelength and polarization. To date, plasmonics have failed to enableenhanced photo sensing capabilities and plasmonic photo sensorsexperience large dissipative losses.

Additionally, although plasmonic sensors have large losses dissipativelosses, plasmonic systems have been developed that contribute toconcentrating incident light in regions adjacent to the systemsupporting the plasmonic excitations. As an example, conduction metallicsheets with subwavelength size partial- or through-holes have been shownto concentrate light within the holes. Mie Photo Sensors, encased in alayer of low-index of refraction insulating material (such silicondioxide) could be combined with such plasmonic systems for enhanceddetection. In addition, it should be noted that other metallic systemsthat have one or more dimensional parameter at or below the wavelengthof incident light, and that are adjacent to the Mie Photo Sensor canhave a similar effect. As an example, this can be achieved by adjustingthe shape, size, or spacing of the metallic contacts on the Mie PhotoSensor.

Improving image quality and shrinking pixel size may drive future photosensor technology adoption. However, a number of these drivers arefraught with tradeoffs between limiters that have negative effects onoptical and electrical performance. For instance, reducing pixel pitch(the center-to-center spacing of pixels, p) can affect the scalingfactor for several metrics driving photo sensor development as shown inTable 1.

TABLE 1 Signal-to-noise ~p⁻¹ Dynamic range ~p⁻² Depth of field ~p⁻¹Depth of focus ~p⁻¹Although there are strong market drivers for reducing pixel size, asthese parameters dependencies show, such a reduction can reduceperformance in other areas.

Generally, improvement in overall image sensor performance from smallpixels has focused on increasing signal and decreasing noise. Much ofthe optimization has been done with improvements in pixel design andprocessing technology at the array level.

IIB. Basic Operation of a Pixel

A pixel is comprised of an individual photo sensor and the signalcollection electronics for operating and reading the photo sensor.Generally, signal collection electronics are co-located with each photosensor. The signal generated from light absorbed by a semiconductor canbe acquired from a measurement of the quantity of charge carrierscreated (a charge-collection, or short-circuit mode) or it can beacquired from a measurement of the voltage across the depletion region(a voltage, or open-circuit voltage mode). In the first case, thegenerated signal is proportional to the incident light intensity, and,in the second case, the generated signal is proportional to thelogarithm of the incident light intensity.

Generally, photo sensors in imaging systems operate in thecharge-collection mode. Operating in charge-collection mode allows thephoto sensor's linear response to incident light to ease data handlingfor image processing and, further, allows photo sensors to be moresensitive to low incident light intensities. In charge-collection mode,charge generated in the photo sensor is collected during a fixedintegration time window and an electrical signal that is proportional tothe total charge accumulated during that window is the reportedmeasurement. As previously described, the charge a photo sensor cancollect is proportional to the area of the sensor. As such, as the photosensor area decreases, the upper end of the sensor's dynamic range fallsin proportion to the square of the pixel's linear size. To counteractthis effect, the integration time can be reduced as the square of pixelsize. Such a time reduction reduces low-light sensitivity and increasesthe complexity and power requirements of both the sensor and theassociated electronics. In addition, as charge-collection mode photosensors shrink, their internal leakage current increases as a proportionof the saturation current. This leakage current acts as a noise sourceand, notably, noise sources place a floor on the lower end of thesensor's dynamic range. Together, these two effects limit the totaldynamic range which, in turn, translates into limits on the scenecontrast that can be captured by the imaging system. Current imagingsystems generally exhibit dynamic ranges of between 60 and 70 dBindicating they capture variations of about 3½ decades in lightintensity.

Photo sensors in imaging systems can use other means to generateimproved signals from light absorbed by a photo sensor. For example, theactive pixel concept, the pinned photodiode pixel, and correlated doublesampling methods have been used to improve light sensitivity and reducenoise in the charge-collection mode. However, despite efforts toincrease light sensitivity, dark current remains a salient factor forsmall pixels in applications which require long integration time and lowillumination. Additionally, even if technological breakthroughs enablefurther reduction in noise sources signal-to-noise ratios, will,generally, continue to worsen as pixel sizes are reduced to dimensionsbelow 1 micron.

Fill factor (i.e., the percentage of light sensitive area in a pixel)directly impacts the sensitivity of a sensor and the signal-to-noise ofthe captured image. There is an inverse relationship between the numberof transistors in a given pixel and its fill factor. In one example, anactive pixel with a pinned photodiode is characterized by 4 transistorsand 5 interconnections in each pixel, resulting in a relatively low fillfactor where the in-pixel circuitry consumes a large amount of spacerelative to the photo sensing area. Low fill factors can be mitigated bysharing some of the control circuitry between multiple pixels, however,this usually means that only the sum of the shared pixels' signal isaccessible.

One method to shrink pixel size and solve the full well capacity problemis to create photo sensors smaller than 1 μm that can only measure thepresence or absence of one, or at most several, photons, but, on theother hand, can be operated at very high speed. At high speeds, themeasurement time is reduced such that the sensors are unlikely tosaturate. The signal generated by the sensors is then composed of thesum of charge collected over many time windows rather than thatcollected during a single time window a. A major drawback of thistechnique is that operating a large number of photo sensors at high dataacquisition rates requires a large amount of power which adds to theoperating costs, and, creates heat which can be difficult to dissipate.

A different approach to increase the dynamic range of image sensorarrays has been to operate them in open-circuit voltage mode.Open-circuit voltage mode delivers a logarithmic response, (i.e.,similar to an eye or of film), instead of the linear response incharge-collection mode. Arrays using open-circuit voltage mode havedemonstrated a dynamic range of over 120 dB, a range of measurable lightintensity spanning six orders of magnitude and approximately twicewhat's achieved in most current detector arrays. However, arrays usingopen-circuit voltage mode have performed poorly at lower lightintensities where their response is dominated by noise.

Another drawback of open-circuit mode photo sensors is that, for pixelslarger than 1 μm, the time constant of silicon semiconductor junctions'voltage-response to light is slow compared to the frame-to-frametransition time. As a result, extra circuitry must be included toforcibly reset each photo sensor before the start of image acquisition.In addition, for pixels larger than 1 μm, the voltage-response time isfrequently longer than the exposure time. This means such pixelsoperated in voltage mode do not reach equilibrium during the exposure.Such dynamic measurements have additional sources of both random noiseas well as difficult to eliminate systematic errors.

II.C Design and Operation of the Imaging Array

Individual photo sensors and pixels can be used as single detectors, oras linear and two-dimensional arrays of detectors. Pixel-to-pixelspacing determines two important parameters in a photo sensor array: theimaging system's spatial resolution in image space and the size of theimaging array for a given number of pixels. The pixel-to-pixel spacingcan place an upper limit on the spatial frequency that can be capturedin the image. This pixel-to-pixel spacing corresponds to a similarspatial-resolution metric in object space. Although, the specific limitdepends on the imaging optics, pixel-to-pixel spacing limits the spatialdetail that can be discerned in the object. Furthermore, aspixel-to-pixel spacing increases, the area of the sensor array increasesby the square of this spacing. Semiconductor device costs riseproportionately to device area, so increases in pixel-to-pixel spacinghas an important impact on imaging array costs.

Many improvements in array design have been driven by the need forsmaller pixels. Optimization of pixels falls into two major categories:(i) improving light sensitivity, and (ii) reducing noise.Light-gathering improvements include micro-lenses, light guides,anti-reflective coatings, thinning interconnect layers and dielectrics,backside illumination, and three-dimensional integration of integratedcircuits or stacked structures to separate photon detection from pixelreadout and signal processing. Many of these same improvements alsoreduce optical cross-talk. Deep trench isolation and buried colorfilters also reduce optical crosstalk and improve the module transferfunction.

Stacked structures in photo sensors can be used to increase theinformation density on the captured image. Multiple frequencies can besimultaneously detected at each imaging point without the need for arealfiltering. Areal filtering removes all but the light of a particularsort “upstream” (i.e., higher in the stacked structure) from aphoto-sensor. Thus, areal filtering removes all other light from theincoming signal. Conversely, stacked photo sensors enable verticalfiltering of color. In this case, color separation arises because thedifferent light wavelengths have different absorption coefficients;however, the different color sensing layers have large contributionsfrom all visible wavelengths. Variable color sensing between layerscontributes to difficulty in resolving color accurately. Implementingstacked structures also has additional information processingchallenges. Because certain wavelengths of light are absorbed to varyingdegrees in all layers, producing a standard Red-Green-Blue image ischallenging. In particular, all the different color contributions fromeach of the layers of the stacked structure are deconvolved beforeforming an image.

In summary, many of the trade-offs in choosing the most suitable camerafor a specific vision application stem from the physics of operation ofthe devices today. Fundamental competing factors define the performanceand they force complex tradeoffs in device, process and circuitry.Limitations on minimum pixel size, sensor dynamic range, and the photosensor's noise characteristics all contribute to generally lowerperformance than is desirable—and, even lower than that achieved usingfilm.

III Mie Photo Sensors

Mie scattering allows small dimensional structures to have optical crosssections larger than their physical cross-sections. As such, Miescattering may enable improvement to photo sensor performance byincreasing light sensitivity, by, for example, concentrating the amountof light available to the photo sensor based on the sensor's opticalcross-section. For example, in Mie scattering, objects with lengthscales on the order of the incident light's wavelength exhibit complexscattering properties that can preferentially direct light toward aphoto sensor. Mie scattering enables a resonance that can be tailored topreferentially interact with specific combinations of incidentwavelength and polarization. Therefore, devices utilizing Mie scatteringcan be used to increase the capabilities of a photo sensor. Further, theconfiguration, design, and characteristics of the structure enabling Miescattering (e.g., structure geometry, structure material(s), and spatialrelationship of features within the structure) can be selected toincrease the capabilities of a photo sensor. Mie scattering is describedin more detail in Section III.A.

Herein, any photo sensor utilizing Mie scattering is described as a Miephoto sensor. A Mie photo sensor enhances photo sensor capability bymeasuring light concentrated internally to a scattering center of thephoto sensor. A scattering center is an area of a Mie photo sensor thatleverages Mie scattering to increase current generation. In an example,a Mie photo sensor includes a scattering center that enhances photondetection. That is, a signal generated by a Mie photo sensor in responseto a photon incident on a scattering center is higher than inconventional photo sensors because of the Mie scattering effect. Thegenerated signal may be subsequently detected in one or more additionalsensors (e.g., as a current, voltage, or resistance).

III.A Mie Scattering

Mie scattering can be described, generally, as a description of theoptical scattering problem that is a general solution to Maxwell'sequations for light scattering from an object. In general, as an objectbecomes much larger than the wavelength of light, the solutions toMaxwell's equations converge with those provided by a physical opticssolution (i.e., as discussed in previous sections). Additionally, as anobject becomes much smaller than the wavelength of light, solutions toMaxwell's equations converge with the Rayleigh scattering approximation.However, in the intermediate region, the scattering solution becomesmore complex and is known as Mie scattering.

For example, light of a given wavelength, λ, will exhibit Mie scatteringfrom an object when that object has a characteristic size in the rangeof about ⅕·λ to about 10·λ. For a sphere of radius r, the characteristicsize is the sphere's circumference, 2πr; for an oblate spheroid it is2πa where a is the spheroid's major axis; and for an infinitely longcylinder of radius r, it 2πr. Finite cylinders of length 2.5r and longerbehave similarly to infinite cylinders. Thus, for visible light,spherical particles with radii between approximately 20 nm and 1.1 μmwill exhibit Mie scattering. The aforementioned shapes are convenientexamples because they have analytical solutions to the opticalscattering problem in this size regime but could be any other shape. Forarbitrary volumes, such as various polyhedrons, only numerical solutionsare available.

A Mie photo sensor can generate signals for image sensing by creatinglarge in-particle fields. Large in-particle fields are possible when thescattering object is large compared to the ratio of the incident light'swavelength to the real part of the index of refraction of the object'sconstituent material (i.e., the object is optically large), smallcompared to the wavelength of the incident light (i.e., the object isgeometrically small), and the scattering object has small attenuationcoefficient compared to 1.

Mie photo sensors are constructed to increase the generation of internalregions of high electric and magnetic fields resulting from thescattering of the incident light. Such fields drive an enhancedabsorption probability and, therefore, an increased photocurrent leadingto improved image generation characteristics. Because such regions ofconcentrated fields are possible in structures thinner than anabsorption thickness, the thickness requirement of conventional photosensors does not apply to Mie photo sensors. Take, for example, a Miephoto sensor whose scattering center is a silicon sphere of radius 100nm for which the characteristic size is 2πr or 628 nm. In this example,600 nm light is incident on the scattering center. For silicon, the realindex of refraction at 600 nm is 3.939 and the attenuation coefficientis 0.02 leading to an absorption length of 4.14×10³ cm⁻¹. Thus, thecharacteristic length of such a sphere is over 4 times larger than theratio of the incident wavelength to its index of refraction. At the sametime, the sphere's attenuation coefficient at its thickest is 0.083.This example illustrates one difference between Mie photo sensors andconventional photo sensors. For example, conventional photo sensors areimplemented so as to maximize their light absorption probability bybeing as thick as possible with a roughly minimum thickness of 1absorption length of the incident light to be measured.

In Mie photo sensors generating large in-particle fields, both thescattered and the absorbed components of the incident energy are small,and the remaining energy is concentrated internally to the scatteringobject. Interference effects can cancel out incident energy in theregions near the scattering object resulting in the object's opticalcross section significantly exceeding its physical cross section. Thatis, effectively, a Mie photo sensor acts as if it absorbs light from astructure much larger than what it actually is.

Mie photo sensors can include scattering centers composed of dielectricmaterials having a real part of their refractive index (the index ofrefraction) that is strongly mismatched with the surroundings and forwhich the imaginary part of the refractive index (the attenuationcoefficient) is small. That is, materials for a Mie photo sensor mayhave a refractive index:{circumflex over (m)}=m+iκ  (2)such thatm>1 & κ<<1  (3)

Examples of such materials include many semiconductors: for example,silicon (m=4.14, κ=0.01), gallium arsenide (m=4.13, κ=0.34), and galliumphosphide (m=3.49, κ=0.003). When semiconductor materials, for example,form objects having sizes suitable for Mie scattering and surrounded bylow index of refraction materials, they can experience extraordinarilylarge internal electric and magnetic fields in response to incidentlight as a necessary consequence of their generation of far-field Miescattering patterns. Some low index of refraction materials forsemiconductors can be, for instance, air (m=1), silicon dioxide (m=1.5),oil, or water. In the case of semiconductor scattering centers, thelarge energy densities formed by these internal fields drive large freecarrier creation. The number of the optically generated free carriers ina Mie photo sensor is, generally, proportional to the incident light'sintensity and can be used in either the charge-collection mode or inopen-circuit voltage mode to drive an output signal that reports theincident light intensity.

Resonances in Mie photo detectors are excitations in response to aspecific, often narrow, range of variables such as, for example,wavelength. As a result, the size of the scattering object can betailored to enhance the sensor's response to a particular wavelengthrange without filtering out other wavelengths. Particular wavelengthresponse provides the opportunity to create photo sensors thatinherently respond to desired wavelengths. Multiple adjacent sensors canbe employed to provide wavelength specificity (either color sensitivityor multi-spectral imaging). In some cases, a broad wavelength responseis desired over a specific narrow wavelength response. Fortunately, inthis case, the resonances can occur in overlapping cascades that enablea broad wavelength response. In general, changing the shape ofindividual conventional photo sensors does not serve as a means ofwavelength or polarization selection. Thus, selecting appropriateshapes, sizes, depths, etc. in Mie photo sensors can be selectwavelengths or polarizations for absorption by the photo sensors.

Resonance overlap can be seen in an example solution to Mie scatteringusing a spherical scattering center. To begin, a Mie solution to theoptical scattering problem expands the electromagnetic field in terms ofan infinite series of orthonormal functions so as to satisfy theappropriate boundary conditions at the scattering object's (e.g., asphere, a polyhedron, etc.) surface. That is, the individual electricand magnetic fields' radial components are 0 and their tangentialcomponents are continuous. In the idealized case of a sphere, theorthonormal basis functions are constructed from complex linearcombinations of the Riccati-Bessel functions; these new functions aredesignated ψ_(n) and ξ_(n) where n designates the order of theunderlying Riccati-Bessel functions and the solution is fully determinedby a series of 4 coefficients for each term in the expansion. Two ofthose coefficients relate only to the electric and magnetic fieldsexterior to the scattering object; the remaining two each indicate theintensity of the electric and magnetic fields respectively inside thescattering object. These coefficients depend on a dimensionless sizeparameter describing the relationship between the scattering object'sphysical size and the light's wavelength:

${x = \frac{2\pi\; r}{\lambda}};$the scattering object's complex index of refraction, m; and, the orderof the expansion: n. In the limit of κ=0, the solution internal to thescattering sphere is given by:

$\begin{matrix}{c_{n} = \frac{{- i}m}{{m\;{\psi_{n}^{\prime}({mx})}{\xi_{n}\left( {mx} \right)}} - {{\xi_{n}^{\prime}\left( {mx} \right)}{\psi_{n}\left( {mx} \right)}}}} & (4)\end{matrix}$where c_(n) is the coefficient describing the intensity of the electricfield; and,

$\begin{matrix}{d_{n} = \frac{im}{{m{\xi_{n}^{\prime}\left( {mx} \right)}{\psi_{n}\left( {mx} \right)}} - {{\psi_{n}^{\prime}\left( {mx} \right)}{\xi_{n}\left( {mx} \right)}}}} & (5)\end{matrix}$where d_(n) is the coefficient describing the intensity of the magneticfield; and where ′ (or “prime”) indicates the derivative with respect tothe whole argument. Lower orders of n (the dipole, quadrupole andoctupole terms: n=1, 2, and 3) generally have the largest impact becausethe lower order orthonormal functions dominate the series expansion andeach term is subsequently multiplied by an additional factorproportional to 1/n in calculating that term's contribution to the totalfield. The coefficients as a function of sphere radius can be plotted tovisualize the realms where the resonances overlap.

FIGS. 1A-1H illustrate a series of resonance plots, according to severalexample embodiments. A resonance plot illustrates the magnitude of anabsorption coefficient as a function of scattering center size. Eachresonance plot includes several different absorption coefficients d1,d2, d3, c1, c2, and c3, calculated according to the definitionsdescribed above. In other words, each resonance plot shows the first 3multipoles (e.g., n=1, 2, and 3) for both c_(n) and d_(n) as functionsof sphere radius. FIG. 1A is a resonance plot 110 for incident lighthaving a wavelength of 400 nm. FIG. 1B is a resonance plot 120 forincident light having a wavelength of 450 nm. FIG. 1C is a resonanceplot 130 for incident light having a wavelength of 500 nm. FIG. 1D is aresonance plot 140 for incident light having a wavelength of 550 nm.FIG. 1E is a resonance plot 150 for incident light having a wavelengthof 600 nm. FIG. 1F is a resonance plot 160 for incident light having awavelength of 650 nm. FIG. 1G is a resonance plot 170 for incident lighthaving a wavelength of 700 nm. FIG. 1H is a resonance plot 180 forincident light having a wavelength of 750 nm.

Mie photo sensors can be many shapes. The example illustrated regardingFIGS. 1A-1E is spherical, however, Mie photo sensors may be rectilinear,close to rectilinear, or some other geometric shape. Rectilinear ornearly rectilinear Mie photo sensors may be created using semiconductorfabrication techniques. In the case of a rectilinear sensor, thesolution to the scattering problem cannot be solved analytically, but itcan be solved numerically.

For example, FIG. 2 illustrates an absorbed power plot for a rectilinearMie photo sensor, according to one example embodiment. The absorbedpower plot 210 shows a numerically calculated ratio of absorbed power toincident power for different wavelengths of light. The absorbed power iscalculated using both (i) Mie solutions for a rectilinear photo sensor(labelled “cube”), and (ii) solutions for the rectilinear photo sensorsas predicted by physical optics calculations (labelled “BL”). Theabsorption coefficients are calculated for two different rectilinearphoto sensors: (i) a first device having 109 nm sides, and (ii) a seconddevice having 218 nm sides. Additionally, the absorption coefficientsare calculated for five different wavelengths of light (e.g., 400 nm,500 nm, 600 nm, 700 nm, and 800 nm).

The absorbed energy of the first device shows the enhanced absorption of400 nm light when accounting for Mie scattering. This is expected giventhe results in the plots of FIG. 1. The absorbed energy of the seconddevice shows a more uniform absorption profile. Notably, several ofthese absorption ratios are greater than 1. The ratio demonstrates thatwhen accounting for Mie scattering, a device has an optical crosssection exceeding its physical cross section.

For comparison, the absorbed energy for the first device as predicted byphysical optics is also shown for both sizes of detectors. In theseexamples, the reduction of absorbed power of a factor of between 4 and 6exists for all wavelengths because of the absence of the internalconcentration arising from Mie scattering.

The results in FIGS. 1A-H and FIG. 2 indicate strategies to both achievebroad wavelength response and to perform multispectral imaging. That is,in a first approach, implementing several Mie photo sensors with sizesand shapes that don't contain a high intensity resonance in either c_(n)or d_(n) allows for a broader wavelength response for a photo sensor. Ina second approach, implementing multiple Mie photo sensors, each withslightly different geometries, located such that each photo sensormeasures similar spatial information in the image plane, allows formultispectral imaging. In this case, signals from the multiple detectorscan be summed, averaged with a uniform weighting, or combined in someother functional form to deliver a desired wavelength response incombination with desired noise and sensitivity requirements.

III.B The Structure and Physics of Mie Photo Sensors

FIG. 3A illustrates top down view of a Mie photo sensor, and FIG. 3Billustrates a side view of a Mie photo sensor, according to one exampleembodiment. In this example, the Mie photo sensor 310 includesrectangular parallelepiped mesas 320 of n-type gallium arsenide. Themesas 320 are sitting on, and attached to, a substrate 330 of intrinsicgallium-arsenide layers. Here, the mesas 320 are an example of ascattering center for a Mie photo sensor. In other embodiments, however,the scattering centers may take any other number of shapes or sizes.

In this example, the mesa 320 is formed by growing a layer of 100 nmthick n-type gallium arsenide on 2000 nm thick intrinsic galliumarsenide substrate 330. Subsequently, a combination of photo-resistapplication, photo-resist patterning with optical lithography and/orelectron-beam lithography, and etching was utilized to fabricate the Miephoto sensor. In this way, the fabrication process removed definedportions of the n-type gallium arsenide leaving behind individual mesas320. The mesa 320 was also fabricated such that each side of the mesawas 250 nm×250 nm. Other examples, such as 500 nm×500 nm sides are alsopossible.

Subsequent processing steps created an ohmic contact 350A and Schottkycontact 350B on the mesa 320. The processing also created conductingtraces to electrically access the contacts 350, although they are notpictured.

The Mie photo sensor 310 could have other dimensionalities or any othernumber of contacts 350. Further, the contacts could be some other typeof contact such as a p-n, or p-i-n, semiconductor junctions.

FIG. 4 illustrates a voltage response plot for a Mie photo sensor,according to one example embodiment. A voltage response plot shows theopen-circuit voltage response between the Schottky contact (e.g., 350B)and an ohmic contact (350A) as a function of incident light intensityfor an Mie photo sensor (e.g., Mie photo sensor 310). In the illustratedexample, the open circuit voltage is shown for both 250 nm square and500 nm square gallium arsenide mesas exposed to normally incident light.Additionally, the estimated Schottky barrier height of the Schottkycontact is 0.48 eV, but could be any other barrier height.

The illustrated example shows enhanced absorption stemming from Miescattering. For example, here, the mesas were exposed to collimatedincident 632.8 nm wavelength light normal to the top surface of the Miephoto sensor. If the physical optics approximation is assumed for thisexample, 37% of the light should be reflected from the surface, and, ofthe remainder, 32% should be absorbed in the mesa for a total absorbedenergy of 21% of the total incident light. However, in this example, themeasured signal indicates that at least twice as much light is absorbedin the Mie photo sensor than expected. That is, there is more absorptionthan expected when assuming the ideal maximum derived using theprinciples of physical optics.

The enhanced response shown in FIG. 4 is illustrative of the internalconcentration effect of Mie scattering described above. Subsequentmodelling results support this conclusion. In example, a dielectricobject can support the internal energy concentration indicative of Miescattering for isolated scattering centers when the dielectric object isin close planer contact with a macroscopically large slab of materialhaving essentially the same complex index of refraction. Energyconcentrations for these dielectric objects indicate that connectedelements fabricated directly from wafers of semiconductor material aresuitable structures for these detectors.

In a conventional photo sensor, mesas (e.g., a Mie scattering sensor) donot exist. Instead, these systems include a thickness of semiconductormaterials acts as an absorbing medium and, at one or more locations,either differentially doped semiconductor or a thin metal layer is usedto establish a depletion region. The depletion regions drive collectionof the locally generated, photo-produced, charges. In the case of anarray, the individual pixels can be, separated by materials to blockexchange of photons or charge. Shrinking an array's areal dimensions sothat individual pixels are smaller than the incident light's wavelengthdoes not yield an array of Mie photo sensors. Further, shrinking thearray thickness so that it is optically thin does not create an array ofMie photo sensors. Generally, small adjacent (traditional) photo sensorsform a larger structure with a continuous index of refraction. Incontrast, in an array of Mie photo sensors, individual photo sensorshave the appropriate dimensions as discussed herein. Further, each Miephoto sensor is largely surrounded by material having a different indexof refraction from the pixel itself to define the scattering center andfurther enable Mie scattering.

Furthermore, generally, individual conventional photo sensors aresurrounded by additional semiconductor materials that support the signalcollection electronics. Upon reducing the photoactive region of thesensor to dimensions of a Mie photo sensor, this additional material incombination with the photoactive region forms a larger structure thatdoes not define a discreet dielectric scattering center as is requiredfor Mie photo sensors.

The Schottky barrier height of a contact in a Mie photo sensor canaffect its operation. For example, FIG. 5 is a voltage multi-responseplot, according to one example embodiment. The voltage multi-responseplot 510 shows a simulated open-circuit voltage for the Mie photo sensorin FIG. 3, but for different barrier heights of the Schottky junction.In the voltage multi sensor plot, the open circuit voltage is measuredfor the same wavelength of light for each Schottky barrier.

As described above, the internal electric and/or magnetic field of a Miephoto sensor is larger than their conventional photo sensorcounterparts. To illustrate, FIG. 6 illustrates a cross-sectional fieldplot of a Mie photo sensor, according to one example embodiment. Thecross-sectional field plot 600 illustrates the electric field in andaround a Mie photo sensor. The illustrated Mie photo sensor is the Miephoto sensor 310 shown in FIG. 3. Additionally, the Mie photo sensor isfabricated on a 1000 nm×1000 nm×200 nm thick Si substrate (e.g.,substrate 330). The Mie photo sensor is subject an incident plane waveof wavelength 600 nm, which induces large electromagnetic fieldslocalized inside the mesa and inside the silicon substrate directlybelow the mesa.

FIG. 7 illustrates a Mie photo sensor, according to one exampleembodiment. In this example, the Mie photo sensor 710 a mesa of silicon350 nm×250 nm×100 nm thick with two metal strips (e.g., contacts 720Aand 720B) forming contacts to the mesa 710. Each of the contacts 720 is250 nm×50 nm×50 nm high. One contact 720A forms a Schottky contact withthe mesa 720, the other contact 720B forms an ohmic contact with themesa. Simulation results of absorbed power as a function of substrateunder the mesa reinforces the result that scattering centers can supportMie scattering induced internal energy concentrations.

FIG. 8 is a cross-sectional field plot of a Mie photo sensor, accordingto one example embodiment. The cross-sectional field plot 700illustrates a cross-sectional view of the Mie photo sensor 710 of FIG.7. The cross-sectional field plots shows the electric field in andaround the device. However, in this example, the Mie photo sensor isfabricated on a 1000 nm×1000 nm×200 nm thick silicon dioxide substratesubject to an incident plane wave of wavelength 600 nm.

In this example, the substrates is silicon dioxide (an insulator),rather than a semiconductor (e.g., silicon). The silicon dioxidesubstrate allows for a discontinuous index of refraction completelyaround the mesa. Additionally, the silicon dioxide strongly supportsreflections of a plane wave incident on the substrate along its frontand back surfaces. Interference effects between the incident and planewaves and reflected plane waves dominate the electric field intensitymap in the substrate and surrounding vacuum. The interference effectsreduce the internal concentration effect in the mesa which is seen in areduction in the maximum electric field intensity. Comparing FIG. 6 andFIG. 8 suggests that the sensitivity of Mie photo sensors on the siliconsubstrate have a minimum sensitivity of between 1 and 2½ orders ofmagnitude lower light level (depending on mesa doping, N_(d)) than doesthe device on the silicon dioxide substrate.

FIG. 9 illustrates a voltage multi-response plot, according to oneexample embodiment. The voltage multi-response plot illustrates theopen-circuit voltage induced between the two metal contacts of the Miephoto sensor in FIG. 5. Here, the voltage response is in response toincident 600 nm light of varying intensities on a Mie photo sensorfabricated using silicon on a silicon substrate. Additionally, in thisvoltage response plot 910, rather than each line conveying a differentSchottky barrier height, each line in the plot represents a differentdoping level of the mesa of the Mie photo sensor. In both a silicon andsilicon dioxide substrate case, the Schottky barrier height is assumedto be 1.0 eV. The Schottky barrier induces a depletion region in thesemiconductor volume adjacent to it and has a built-in voltage thatreflects the equilibrium state of the system. The addition ofphoto-produced electron-hole pairs changes this built-in voltage whichis measurable as the open-circuit voltage between the two metalcontacts. The open-circuit voltage is proportional to the log of theproduction rate of photo-generated carriers.

A Mie photo sensor on a silicon substrate is, generally, more sensitivethan a Mie photo sensor on a silicon dioxide substrate and indicates theimportance of mesa and substrate composition. There are other ways ofenhancing optical detection performance (e.g., sensitivity) as well. Oneexample is to decrease the area of the Schottky contact. Decreasing theSchottky contact area can reduce the saturation current across thebarrier and this significantly increases the device sensitivity.Further, decreasing the Schottky contact area can enable engineering ofthe free carrier gradient and thereby control the diffusion rates.Controlling diffusion rates enables control over cross-talk betweensensors on a non-insulating substrate such as intrinsic silicon. Inaddition, changing the size and shape of the metal contacts can serve tofurther define the interaction between the detector and the incomingwave.

FIGS. 10A-10C illustrate various configurations of a Mie photo sensor,according to some example embodiments. Each of the figures illustrates adifferent configuration of Mie photo sensor, but all of the Mie photosensors at least include a substrate (not illustrated, for clarity). Thesubstrate is a material layer having a first index of refraction andcomprising a mesa 1020 of semiconducting material. The mesa has a secondindex of refraction and is configured to generate free carries withinthe semiconducting material in response to an electromagneticperturbation (e.g., visible light, x-rays, infrared radiation, etc.).The mesas 1020 are surrounded by a refractive medium 1040 (e.g., air)having a complex (e.g., third) index of refraction. Generally, the thirdindex of refraction is lower than the first and second indices ofrefraction. In some cases, where the material of the mesa and thesubstrate are similar, or the same, the index of refraction for the twomaterials may be similar, or the same.

Together, the refractive medium 1040 and the mesa 1020 (and/orsubstrate) form an interface with an index of refraction across theinterface that is discontinuous. That is, the refractive medium 1040 maycomprise some material which has a different real part of the refractionindex than does the mesa 1030. Ideally, the discontinuity refractiveindex should be as large as possible across the boundary between themesa 1030 and the refractive medium. For example, in the case of arectilinear silicon mesa with air on 5 sides, the refractive indexdiscontinuity between the mesa and the air refractive medium is between5.3 and 3.7 across the visible spectrum. In the case of gallium arsenidesubject to 546 nm incident light, refractive index discontinuity betweenthe mesa and the refractive medium is 4.0.

The, the mesa of semiconducting material within the refractive mediummay form an electromagnetic scattering center for the Mie photo sensor.In some cases, the scattering center may be some portion of the mesarather than the entirety of the mesa. In other words, the mesa may bedescribed as having a geometric shape with a set of boundaries, and theelectromagnetic scattering center may be any portion of thesemiconducting material of the mesa within, and up to, those boundaries.

The Mie photo sensors include at least one contact 1050 (e.g., contacts1050A and 1050B) contacting the mesa 1020. The contacts 1050 may be anycombination of ohmic contacts, Schottky contacts, p-n junctions, orp-i-n junctions. In a configuration where both contacts 1050 are Ohmic,at least one of the interfaces between the refractive material (orsubstrate) and the mesa 1030 is a Schottky barrier.

In various configurations, Mie photo sensors 1010 may include asymmetricmesas which can be used to change the photo sensor's response topolarization of the incoming light. Highly asymmetric mesas will presentdifferent effective spatial dimensions to light with differentorientations of its constituent fields. For example, the Mie photosensors 1010 in FIGS. 10A-10C show mesas 1020 with different aspectratios in relation to both the incoming light and to the contacts. Inthis way, particular polarization states of the incoming light can beindividually measured, and/or particular wavelengths of incoming lightcan be resonant in the photo sensor. Polarization dependent measurementscan deliver important information about the composition of lightreflecting or light emitting objects.

Mie photo sensors can be configured to absorb designed a particularwavelength of light. For example, the size, shape, material, etc. of ascattering center can be configured to absorb a particular wavelength.In this case, Mie scattering absorbs the particular wavelength ofelectromagnetic perturbation at a resonance level and generates a firstamount of free carries corresponding to the resonance level. Theelectromagnetic scattering center may also absorb different wavelengthsof electromagnetic perturbation at non-resonance levels and generate asecond amount of free carriers corresponding to the non resonance level.The number of free carriers generated from light at the particularwavelength (e.g., resonance) is greater than the number of carriersgenerated from carriers at different wavelengths (e.g., non-resonance).

Generally, an individual Mie photo sensor is configured to a narrowwavelength response, but multiple Mie photo sensors can be configuredfor different wavelength responses such that an array of Mie photosensors absorb a broad range of wavelengths. In this way, the intensityvariation as a function of wavelength can be discerned for severalspectrums of incoming light.

These configurations of Mie photo sensor presented herein are given asmeans of example and are not intended to be limiting. More specificallya Mie photo sensor can be any configuration of photo sensor thatutilizes Mie scattering to enhance photo-current generation in a photosensor.

For example, a Mie photo sensor can have various types of substrates.Some example substrates include: carbon (e.g., diamond, and diamond withnitrogen vacancies, etc.), gallium arsenide, mercury cadmium telluride,platinum silicide, germanium, thallium bromide, etc. Further, each ofthe substrate materials may be selected such that the Mie photo sensoris configured have a resonance for a particular type of electromagneticperturbation. For example, Mie photo sensors including a substratecomprising (i) carbon may have a UV an X-ray resonance, (ii) mercurycadmium telluride may have a broad infrared resonance, (iii) platinumsilicide may have an infrared resonance, (iv) germanium may have a gammaray resonance, and thalium bromide may have an x-ray resonance.

As another example, a Mie photo sensor may have a height between 30 nmand 1700 nm. Where the height of the Mie photo sensor is measured in aperpendicular direction relative to the surface of the substrate. Again,the height of the Mie photo sensor can influence the particularwavelength of electromagnetic perturbation that causes a resonance infree carrier generation, and/or a particular polarization of light thatcauses a resonance in free carrier generation.

As another example, a mesa may have different planar sizes. Toillustrate a mesa may have a first feature in a first direction between10 nm and 800 nm and a second feature in a second direction between 10nm and 800 nm, where the first and second directions are approximatelyorthogonal to one another. Again, the size of the first feature and thesecond feature can influence the particular wavelength ofelectromagnetic perturbation that causes a resonance in free carriergeneration, and/or a particular polarization of light that causes aresonance in free carrier generation.

III.C Basic Operation of the Mie Photo Sensor Pixel

Mie photo sensors, like conventional photo sensors, can be deployed aspixels in imaging systems operating in either open-circuit orcharge-collection mode.

As previously discussed, a non-ohmic contact may either be formed from aSchottky junction or a p-n junction. The advantage of Schottky junctionsis that they provide very fast response times. Previously, Schottkyjunctions were seldom used in photo sensors because they typically havea higher dark current, which establishes an intensity floor below whichmeasurements cannot be performed. In a Mie photo sensor, however, thearea of the metal-semiconductor interface can be made extremely smallwhich strongly reduces the junction dark current.

Mie photo sensors are attractive for deployment in the open-circuit modebecause of the photo sensors fast response time and low minimumsensitivity. The fast response time enables equilibrium voltagemeasurements and the lower minimum sensitivity allows the voltagemeasurements to extend to lower incident intensities. Photo sensorsoperated in this mode have inherently large dynamic ranges due to thismode's logarithmic response; the improved minimum sensitivity suggeststhey can deliver a dynamic range significantly larger than the 6 decadesdemonstrated in other logarithmic detectors.

Another benefit of Mie photo sensors utilized in voltage mode is theycan be operated without a bias voltage and without reset circuitry. Thefast response possible with a Schottky contact, in combination with thesmall area contact enabled by the Mie photo sensors' small size, makesit possible to implement a direct voltage measurement of the Mie photosensor's response to light without the need to add reset circuitry tothe pixel.

FIGS. 11A-11E illustrate several different configurations for a pixel inan image sensor including one or more Mie photo sensors, according tovarious example embodiments. Each pixel 1110 comprises a mesa ofsemiconducting material 1120, a substrate 1130, a refractive material1140 (air, as illustrated), and one or more contacts 1150. Further eachof the pixels include some combination of control electronics to readinformation from, and control the pixel.

FIG. 11A illustrates an example pixel of an image sensor array includinga Mie photo sensor, according to one example embodiment. In thisexample, the pixel 1100A comprises a single selection transistor 1160connecting the column bus 1180 to the Mie photo sensor 1110. Becausethere is only a single selection transistor 1160, the pixel 1160 and Miephoto sensor 1110 deliver inherently low-power performance.

FIG. 11B illustrates an example pixel of an image sensor array includinga Mie photo sensor, according to one example embodiment. In thisexample, the pixel sensor includes both a selection transistor 1160 andan amplifying transistor 1162. This configuration allows for theisolation of the capacitance of the Mie photo sensor from the rest ofthe column bus 1180 (and remaining readout circuitry). In addition, thisconfiguration allows for the pixel to rescale (via the amplifyingtransistor 1162) the voltage output from the Mie photo sensor.

FIG. 11C illustrates an example pixel of an image sensor array includinga Mie photo sensor, according to one example embodiment. In thisexample, the pixel includes a selection transistor 1160, an amplifyingtransistor 1162, and a capacitor 1164. Here, the output voltage can betemporarily stored across an appropriately sized capacitor 1164. Thecapacitance of the capacitor 1164 depends on the voltage difference ofthe circuitry (typically V_(DD)), the resistance of the readoutcircuitry, and the desired time response. This configuration of a pixeladditionally allows for all the pixels in the array to be measurednearly simultaneously.

FIG. 11D illustrates an example pixel of an image sensor array includinga Mie photo sensor, according to one example embodiment. In this casethe pixel includes a selection transistor 1160, an amplifying transistor1162, a capacitor 1164, and a reset transistor 1166. This configurationallows the pixel to reset the capacitor to its zero voltage differencestate. Alternatively, or additionally, this configuration allowsswitching between a readout mode mediated by the voltage storingcapacitor and one that is not. As an example of operation, when theselection transistor 1160 is “OFF,” turning the reset transistor 1166 onserves the reset function. When the selection transistor 1160 is “ON,”turning the reset transistor 1166 on serves to largely bypass thevoltage storage capacitor.

FIG. 11E illustrates an example pixel of an image sensor array includinga Mie photo sensor, according to one example embodiment. As describedabove, in a Mie photo sensor with a Schottky junction, the response timeof the Mie photo sensor is rapid. Accordingly, in cases where a p-njunction is used, an option to reset the sensor to its dark state may bedesired. For example, here, the pixel 1110 includes a reset switch 1168.

FIGS. 11A through 11E are meant for illustrative purposes, and manyother configurations are of pixels including Mie photo sensors are alsopossible. Additionally, any of combination of the functionalitydescribed above may be included in various pixels.

For Mie photo sensors implemented in the charge-collection mode, asmaller photo sensor size reduces the charge-collection time, therebyenabling increased frame rates. In addition, a reduction in saturationcurrent makes the use of Schottky junctions (in place of semiconductorjunctions) more widely feasible. Schottky junctions have inherentlyhigher saturation currents then do semiconductor junctions which sets acorrespondingly higher minimum sensitivity for photo sensors utilizingmetal-semiconductor rectifying interfaces. In some exampleconfigurations, however, Mie photo sensors utilizing Schottky junctionshave much faster response times which enables higher frame rates and thedetection of short-period optical events.

Mie photo sensors can also be implemented in charge-collection mode withcircuitry similar to that of pinned photo diodes. However, inopen-circuit configurations, the absence of a transfer transistorbetween the photoactive sensor and the other in-pixel circuitry canresult in improved performance by, for example, reducing dark currentissues.

Mie photo sensors' optical cross-section exceeding their physical crosssection means that Mie photo sensors can respond to the incident lightthat would normally strike the regions around and adjacent to thephotosensitive are of the detector. This increases the effective fillfactor of the imaging chip. Such regions can be occupied by the controland processing electronic circuitry. Such electronics can be used toenhance signal collection and amplification, for instance byimplementing faster circuitry for high speed imaging or for enablingglobal, versus rolling shutter data collection and transfer.

III.D Design and Operation of the Mie Photo Sensor Array

Individual Mie photo sensors can be implemented as single sensor imagingdevices using the same technique employed with an individualconventional photo sensor. In this case, the sensor is scanned acrossthe image plane formed by a static object in order to construct animage. Again, as with conventional photo sensors, images may be formedby linear arrays of identical Mie photo sensors scanned across the imageplane or by two-dimensional arrays of stationary Mie photo sensors. Likeconventional photo sensor arrays, the pixel-to-pixel spacing can placean upper limit on the spatial frequency that can be captured in theimage. This pixel-to-pixel spacing corresponds to a similarspatial-resolution metric in object space. Where direct imaging, withoutintervening optics, is used, the concept of a diffraction limit or Airydisk doesn't exist. Examples of such imaging include holography andcontact imaging. The inability to provide finely spaced photo sensorshas limited the widespread application of these techniques in manysituations where they might be of value. In the case where optics isrequired, the limit of the spatial resolution of the object is afunction of the optics transferring light from the imaged object to theimage. For a given optical system, large pixel-to-pixel spacing canfurther limit the spatial detail that can be discerned in the object.For this reason, Mie photo sensors can also deliver improved spatialresolution when used in combination with imaging optics because of theirreduced size and increased fill factor.

All the advantages of Mie photo sensors over conventional photo sensorsdiscussed above can contribute to improved imaging performance in eachof these cases. In addition, Mie photo sensor pixels are all compatiblewith image array enhancement methods currently used with conventionalphoto sensors. These methods include light-gathering improvements andnoise reduction techniques such as micro-lenses, light guides,anti-reflective coatings, thinning interconnect layers and dielectrics,backside illumination, three-dimensional integration of integratedcircuits, or stacked structures to separate photon detection from pixelreadout and signal processing, double sampling methods, etc.

Several characteristics of Mie photo sensors each enable new ways toarrange and to use photo sensor arrays (either one-dimensional,two-dimensional or three-dimensional arrays). The characteristics caninclude, for example, a possibility of the Mie photo sensor size beingsmaller than the incident light's wavelength, a possibility of theoptical cross section of a Mie photo sensor exceeding their physicalcross section, and a possibility of designing the Mie photo sensor toexhibit resonances in wavelength and/or polarization, and the like.Taken together, these characteristics allow for new and powerful arraydesigns.

Unless subwavelength diffraction effects are used in the image analysis,the meaningful grid for display or analysis purposes is one with gridnodes separated by a minimum of about one Airy disk diameter. Mie photosensor sizes that are smaller than the wavelength of light make possiblemultiple measurements of each resolvable spot, or Airy disk, in theimage. This holds independent of the f-number of the optics used to formthe sought-after image. This rebinning of the spatially distributedintensity measurements can be thought of as defining effective pixels.Such effective pixels could be made larger than an Airy disk as well. Inthat case, the spatial frequency spectrum of the system's optics must beconsidered to minimize aliasing in the image. The spatial resolution ofthe image space is the resolution implied by the effective pixeldistribution. The signal from the physical pixels within an effectivepixel can be combined or kept separate.

Combining the signal from different photo sensors has been shown tosubstantially improve the signal-to-noise ratio in the final image ascompared to using the signal from a single larger pixel that is the areaof the sum of the smaller ones. This improvement is especially apparentat low light levels. With Mie photo sensors this can occur withoutcompromising the image quality. In addition, with larger pixels suchcombinations, or upscaling, would result in the introduction of opticalartifacts from aliasing. Mie photo sensors below the size of the Airydisc enables combining sensors without the presence of the highfrequency optical components that lead to aliasing.

In some examples, signals from sensors within a single effective pixelare to be combined using on-chip electronics, off-chip electronics, orperformed in software. When using on-chip electronics, combining signalscan result in substantial reductions of on-chip circuitry. Combiningsignals do not have to be made using photo sensors on a regular grid.For instance, increasing the effective pixel area from the image arraycenter to the edges yields a foveated pattern similar to that of thehuman eye. One advantage of irregular photo sensor patterns is they candeliver a higher spatial resolution signal at one or more parts of theimage, but a lower noise and a higher dynamic range signal at otherparts of the image.

Generating signal combinations generally reduces the data throughputrates and, particularly, reduces throughput rates for on-chip combining.However, data combination in software has advantages in flexibility. Incases where the objects in the image have unknown sizes or features,feedback or machine learning can be used to determine those objects. Forexample, different combinations of physical pixels can be combined intoeffective pixels in order to maximize detection and evaluationeffectiveness.

Alternatively, keeping signals generated by the photo sensor separateenables multiple wavelength and/or polarization measurements of theincident light within each effective pixel. For example, in imagesensors where the individual pixels are selecting pixels (designed toselect specific wavelengths or polarizations), it may be advantageous toreduce signal combinations between different types of selecting pixels.In this way, each set of pixels with the same selection mechanism can beused to form an image with the spatial resolution of the effectivepixel.

In some configurations, Mie photo sensors fabricated of the samematerial can be stacked such that each Mie photo sensor has a highabsorption probability for light in a desired range of wavelengths whilesimultaneously remaining largely transparent to other wavelengths. Inthis way, the imaging array can more efficiently use the incomingsignal. In addition, smaller pixels can be used, facilitating collectingboth higher frequency spatial information and collecting a largervariety of wavelength information. With such smaller pixels, the Miephoto sensors' semiconductor junction area can be vastly reduced,decreasing the junction saturation current and, in turn, reducing thesensors' minimum sensitivity. Increased efficiency can result in lowernoise, lower intensity thresholds, or smaller array areas. Stacked photosensors can also enable utilization of chromic aberrations that occur inimaging systems. Chromic aberration results in different colors from theobject plane coming to a focus in different image planes. Such anarrangement allows for less expensive and complex optics or,alternatively, higher resolution images. By designing optics withengineered chromic aberration, color images without any color filteringbecomes possible.

III.E Performance Improvement from Mie Photo Sensors

Mie photo sensors overcome constraints currently seen with conventionalphoto sensors in at least three areas: 1) image quality, 2)three-dimensional pixel size, and 3) functionality.

Mie photo sensors have a significant impact on image quality becausethey can improve measurement sensitivity, dynamic range, and responsetime relative to traditional photo sensors. Under a variety ofimplementation configurations, they can be used to further reduce noise,to enhance spatial resolution and to improve image contrast.Furthermore, they eliminate critical challenges that arise in the use ofsmall pixels in applications which require long integration timesarising from low illumination.

Mie photo sensors solve the challenges to substantially reducing thethree-dimensional size of the pixel. Mie photo sensors are fabricated atsizes transverse to the incident light on the order of, or smaller than,the wavelength of light to be detected. Equally important, Mie photosensors are able to be implemented with a thickness less than 1/α. Inconjunction with current semiconductor planarization techniques, arraysof such thinner photo sensors deliver a smaller depth of focus which inturn eases utilizing such small pixels.

Mie photo sensors also improve functionality in a number of criticalways. First, Mie photo sensor has a significant impact SWaP. Smaller andthinner arrays can translate into utilization of smaller f-number opticsfor some applications. Smaller f-number optics can be significantly morecompact. Mie photo sensors reduce power consumption of each pixel so asto reduce the overall power requirements of the imaging device or,alternatively, to enable an increase in pixel count while minimizing theincrease in power consumption.

Additionally, Mie photo sensors exhibiting different resonances inwavelength or polarization mean that different sensors can have anintrinsic sensitivity to light of different types. Using conventionalphoto sensors, wavelength or polarization specificity is achieved usingfiltering. This approach removes the incident, information bearing,light except that of a specified type. Rather than eliminating the otherlight, Mie sensors can be thought of as extracting the specified lightfrom the incoming stream and allowing either nearby, adjacent, ortrailing Mie photo sensors to continue to measure other aspects of thelight. Mie photo sensors exhibiting a resonance to one or more featuresof incident light are therefore referred to as selecting Mie photosensors. As such, it becomes possible to develop compact, low powerdevices using Mie photo sensors for image detection and chip levelintegration of multiple, high resolution, imaging modalities for rapiddata collection of fast-moving scenes.

Further, Mie photo sensors can reduce many of the fill factor issuesseen with conventional sensor technologies where the percentage of lightsensitive area in a pixel directly impacts the sensitivity of a sensorand the signal-to noise of the captured image. As such, there is greateropportunity to embed computer vision pre-processing functions on thechip while limiting expansion of sensor size and power consumption.

III.F Applications

The small size, high speed, and compatibility with silicon fabricationtechnology suggests that Mie photo sensors could be implemented, assingle detectors or arrays of detectors, as the receiver for opticallytransmitted signals. In particular, Mie photo sensors could befabricated as part of individual integrated circuits making up computercomponents thereby simplifying the increase in information transferrates within components, between components on the CPU board and oncomputer backplanes.

The advantages of imaging with optics or contact imaging with a Miephoto sensor array include increased spatial resolution, increasedcontrast, smaller camera packages, spectral sensitivity,polarization-based imaging, imaging with lower power input requirements,etc. These advantages deliver enhanced performance in many applicationsincluding imaging for consumer electronics, medical imaging forendoscopy and surgical robotics, industrial imaging and machine vision,imaging for automotive applications including self-driving cars, andimaging for security and defense applications.

The high speed of the Mie photo sensor suggests it has particular valuefor optical time-of-flight measurements. Individual Mie photo sensorscould be implemented as part of object tracking and crash prediction.Implemented as arrays, Mie photo sensors could be utilized in this wayas a means of three-dimensional scene reconstruction.

The low light sensitivity in combination with the logarithmic responseof Mie photo sensors implemented in the open-circuit mode suggestsutility for imaging in near dark to bright light conditions. Such arange is frequently found in automotive cameras, surveillance imagingtools, and many industrial applications.

What is claimed is:
 1. A Mie photo sensor comprising: a material layerhaving a first index of refraction and comprising a mesa ofsemiconducting material, the mesa configured to generate free carrierswithin the semiconducting material in response to an electromagneticperturbation; a refractive medium surrounding the material layer andhaving a complex index of refraction, the refractive medium and mesaforming (i) an interface with an index of refraction across theinterface that is discontinuous, and (ii) an electromagnetic scatteringcenter configured for generating free carriers via optical absorptionand Mie resonance of the electromagnetic perturbation at the scatteringcenter; and one or more electrical contacts coupled to the mesa andconfigured to sense free carriers generated within the scattering centerin response to the electromagnetic perturbation.
 2. The Mie photo sensorof claim 1, wherein the mesa of semiconductor layer forms a geometricshape having a set of boundaries, and the electromagnetic scatteringcenter is formed at the boundaries such that the electromagneticscattering center comprises the semiconducting material of the mesa. 3.The Mie photo sensor of claim 1, wherein the mesa of semiconductingmaterial forms a geometric shape having a set of boundaries, and theelectromagnetic scattering center is formed within boundaries such thatthe electromagnetic scattering center comprises some portion of thesemiconducting material of the mesa.
 4. The Mie photo sensor of claim 1,wherein the mesa of semiconducting material is doped silicon.
 5. The Miephoto sensor of claim 1, the mesa of semiconducting material is a dopedsemiconductor material, including any of: gallium arsenide, galliumphosphide, gallium nitride, cadmium telluride, or cadmium sulfide. 6.The Mie photo sensor of claim 1, wherein the material layer comprisessilicon.
 7. The Mie photo sensor of claim 1, wherein the material layercomprises silicon dioxide.
 8. The Mie photo sensor of claim 1, whereinthe material layer comprises a semiconductor material.
 9. The Mie photosensor of claim 1, wherein the material layer comprises an insulatingmaterial.
 10. The Mie photo sensor of claim 1, wherein the materiallayer comprises any of: carbon, gallium arsenide, mercury cadmiumtelluride, platinum silicide, germanium, or thallium bromide.
 11. TheMie photo sensor of claim 1, wherein the mesa of semiconducting materialhas a height of 50 nm and 250 nm., the height measured in aperpendicular direction relative to a surface of the material layer. 12.The Mie photo sensor of claim 1, wherein the mesa of semiconductingmaterial has a feature size between 10 nm and 80 nm in a first directionfeature size between 10 nm and 80 nm in a second direction, the firstand second direction orthogonal to one another and parallel to a surfaceof the semiconductor layer.
 13. The Mie photo sensor of claim 1, whereinthe electromagnetic scattering center is configured to absorb aparticular wavelength of electromagnetic perturbation, and a size of theelectromagnetic scattering center is proportional to the particularwavelength of electromagnetic perturbation.
 14. The Mie photo sensor ofclaim 13, wherein the proportionality between the size of theelectromagnetic scattering center and the particular wavelength ofelectromagnetic perturbation is based on any of: the size of theelectromagnetic scattering center, the particular wavelength ofelectromagnetic perturbation, the complex index of refraction, and thefirst index of refraction.
 15. The Mie photo sensor of claim 1, whereinthe electromagnetic scattering center is configured to absorb aparticular polarization of electromagnetic perturbation, and a size ofthe electromagnetic scattering center is proportional to the particularwavelength of electromagnetic perturbation.
 16. The Mie photo sensor ofclaim 15, wherein the proportionality between the size of the scatteringcenter and the particular polarization of electromagnetic perturbationis based on any of: the size of the electromagnetic scattering center,the particular polarization of electromagnetic perturbation, the complexindex of refraction, and the first index of refraction.
 17. The Miephoto sensor of claim 1, wherein: the mesa of semiconducting materialhas a second index of refraction, and the complex index of refraction isless than the first index of refraction and the second index ofrefraction.
 18. The Mie photo sensor of claim 17, wherein the firstindex of refraction is the same as the second index of refraction. 19.The Mie photo sensor of claim 1, wherein the refractive medium issilicon dioxide.
 20. The Mie photo sensor of claim 1, wherein therefractive medium is a low index of refraction material including anyof: air, oil, or water.
 21. The Mie photo sensor of claim 1, wherein afirst contact of the one or more of the electrical contacts forms anOhmic contact with the mesa of semiconductor material and a secondcontact of the one or more electrical contacts forms a Schottky barrierwith the mesa of semiconductor material.
 22. The Mie photo sensor ofclaim 1, wherein a first contact of the one or more of the electricalcontacts forms an Ohmic contact with the mesa of semiconductor materialand a second contact of the one or more electrical contacts forms a p-njunction with the mesa of semiconductor material.
 23. The Mie photosensor of claim 1, wherein a first contact and a second contact of theone or more of the electrical contacts form an Ohmic contact with themesa of semiconductor material.
 24. The Mie photo sensor of claim 23,wherein the Mie photo sensor includes a p-n junction at a boundarybetween the refractive material and the mesa of semiconducting material.25. The Mie photo sensor of claim 1, wherein: the electromagneticscattering center absorbs a particular wavelength of electromagneticperturbation at a resonance level and generates a first amount of freecarriers corresponding the resonance level, the electromagneticscattering center absorbs a different wavelength of electromagneticperturbation at a non-resonance level and generates a second amount offree carriers corresponding to the non-resonance level, and the firstamount of free electrons is greater than the second amount of freeelectrons.
 26. The Mie photo sensor of claim 1, wherein the opticalabsorption per unit volume of the electromagnetic perturbation in theelectromagnetic scattering center is higher than the optical absorptionper unit volume of the electromagnetic perturbation in both thesemiconductor layer and the refractive medium.
 27. The Mie photo sensorof claim 1, wherein: a first amount of free carriers per unit volumegenerated by the absorption of the electromagnetic perturbation in theelectromagnetic scattering center, a second amount of carriers per unitvolume are generated by the electromagnetic perturbation in thesemiconductor layers, and the first amount of free carriers per unitvolume is greater than the second amount of free carriers per unitvolume.